Citations: Springer-Verlag - Berger (ResearchIndex)

47 citations found. Retrieving documents...

M. Berger, Geometry, Springer Verlag, Berlin (1987).

Home/Search Document Not in Database Summary Related Articles Check

This paper is cited in the following contexts:

First 50 documents

Simulating Non-Lambertian Phenomena Involving Linearly-Varying.. - Chen, Arvo (2001) (3 citations) (Correct)

.... [11] As for the axial moment # about a unit vector v, Arvo [2] has shown that it reduces to a one dimensional integral by (A, v) # where p = 0 when n is even, and p = 1 when n is odd, and # 1 (A) 0 and (A) #(A) which can be computed either from Girard s formula [4, 2] or a boundary integral formula for #(A) 6, 5] From the above edge parameterization, the complete integral in equation (16) can be evaluated exactly in O(nk) time for a k sided polygon, by computing the function F (n, x, y) # d# incrementally according to the following recurrence identity ....

Marcel Berger. Geometry, volume 2. Springer-Verlag, New York, 1987. Translated by M. Cole and S. Levy.

Quaternion Gauss Maps and Optimal Framings of Curves and Surfaces - Hanson (1998) (Correct)

....the quaternion Gauss map, a subspace of the space of possible quaternion frames of the object to be visualized. Mathematically speaking, the space of possible frames is the circular Hopf fiber lying above the point in S corresponding to each specific curve tangent or surface normal (see, e.g. [39, 3]) For space curves, specifying a frame assignment as a quaternion path leads at once to tubular surfaces that provide a thickened representation of the curve that interacts well with lighting and rendering models. For surface patches, the approach results in a structure equivalent to that of ....

.... are nontrivial quadratic forms constructed from all the quaternion components; however, a projection to a subspace of the quaternion space based on the bilinear action of quaternions on pure vectors may be constructed by imitating the projection of the Hopf fibration of S (see, e.g. Shoemake [39, 3]) In Figure 15, we show two such cases, an ellipsoid with orthonormal polar coordinates singular at the poles and a torus with global, nonsingular, coordinates, using our now standard projections of the quaternion Gauss map to 3D. In each of these cases, a single circuit of the surface generates ....

[Article contains additional citation context not shown here]

BERGER, M. Geometry I, II. Springer Verlag, Berlin, 1987.

On a Special Arrangement of Spheres - Hiroshi Maehara And (Correct)

....tangent spheres are called escribed spheres of #. Every triangle has exactly four tangent circles. For n 3, the number of distinct tangent spheres of an n simplex depends on the shape of the simplex. The number of tangent spheres of a tetrahedron in R can vary from 4 to 8, see, e.g. Berger [2] p.296. ## ## # # # # # # # Figure 2: The circumscribed circle and an escribed circle of a triangle It is obvious that in the plane case, the circumscribed circle of a triangle always cuts all escribed circles of the triangle, see Figure 2. Then, for n 3, is there an n simplex that ....

M. Berger, Geometry I, New York (1987) Springer-Verlag.

Non-overlapping Constraints between Convex Polytopes - Beldiceanu, Guo, Thiel (2001) (Correct)

....cases: the non overlapping constraint between two convex polygons as well as the non overlapping constraint between d dimensional boxes. 1 Introduction The first part of this paper introduces necessary conditions for the non overlapping constraint between convex polytopes. A convex polytope 1 [3] is defined by the convex hull of a finite number of points. Non overlapping detection between fixed objects is a fundamental geometric primitive that arises in many applications. However from a constraint perspective it is natural to extend the previous problem to a non overlapping constraint ....

Berger, M.: Geometry II, Chapter 12. Springer-Verlag, 1980.

Single View Metrology - Criminisi, Reid, Zisserman (1999) (30 citations) (Correct)

....space. The error analysis has been validated by using Monte Carlo statistical tests. Examples have been provided to show the computed measurements and uncertainties on real images. More generally, ane three dimensional space may be represented entirely by sets of parallel planes and directions [Ber87]. We are currently investigating how this full geometry is best represented and computed from a single perspective image. 6.1. Missing base point A restriction of the measurement method we have presented is the need to identify corresponding points between planes. One case where the method does ....

M. Berger. Geometry II. Springer-Verlag, 1987.

Line Segment Rasterization in N-Dimensional Space - Wuthrich (1994) (Correct)

....the vector v, i.e. the set A v = fw 2 R n j w = a v; a 2 Ag, we have 4 that V = VO . The closures of the Voronoi sets associated with a lattice tessellate the n dimensional space. A tessellation of the n dimensional space is the generalization of a tiling in a two dimensional space [6, 12]. More precisely, a tessellation in the n dimensional space consists of a connected compact subset A ae R n and a subgroup G of the group of orientation preserving isometries of R n , such that the interior A of A is non empty and such that the following conditions are satisfied: S g2G ....

Berger, M. Geometry, vol. I--II. Springer Verlag, Berlin, 1987.

Improved Bounds on Weak epsilon-Nets for Convex Sets - Chazelle, Edelsbrunner.. (1994) (Correct)

....ugly. Strikingly, the proof is completely 10 trivial in hyperbolic geometry, which thus appears to be its natural habitat. To provide a better understanding of what is happening and make the presentation selfcontained, we begin with a brief overview of the geometry of the hyperbolic plane. See [4, 7, 9, 10, 12, 14, 15] for background material. 5.1 Hyperbolic Geometry Euclid s fifth postulate states that through a given point exactly one line can be parallel to another given line. Hyperbolic geometry postulates that an infinite number of such lines exist. For our purposes the most interesting consequence of ....

Berger, M. Geometry II, Springer-Verlag, 1987.

Critical Sets of Smooth Solutions to Elliptic.. -.. (1995) (Correct)

.... [CF] and various interesting estimates for the n Gamma 1 dimensional Hausdorff measure of this set have been achieved [CM, DF1, DF2, DF3, HS, L, N] In other works concerning u Gamma1 f0g the behaviour of u near a zero is investigated showing that u can be approximated by certain polynomials [Al,B, HOHO1, HOHO2, HOHON, R]. For all such investigations the critical zero set Sigma 0 : u Gamma1 f0g jruj Gamma1 f0g Supported by Federal Ministry of Science of Research, Austria. It is a pleasure to thank P. Michor and N. Nikichin for helpful discussions. Typeset by A M S T E X 2 plays an important role. But ....

....ff in C 3 . If j , 1 j 3, is a dual basis in C 3 , then ff has the form Sigma 3 j=1 2 j . Let fl ae P (C 3 ) be the set of tangent planes to the characteristic surface N (p)n Sigma(p) Evidently, the characteristic property of the surface implies that fl ae im(ff ) see [B], ch.14.5) Since im(ff ) is an algebraic curve in P (C 3 ) we have: either fl is a point and thus p is linear, or fl coincides with im(ff ) In the last case it follows from Proposition 3.2(i) that fl is the image of the quadric Sigma 3 j=1 2 j and hence p = const Sigma ....

M. Berger, Geometry II, Universitext, Springer Verlag, Berlin, 1987.

Partitioning the Sphere With Constant Area Quadrangles - Lemaire, Weill (2000) (Correct)

....the mesh of a laser target. We have found no references on this problem in the literature. However, the ve regular polyedra octahedron, cube, tetrahedron, dodecahedron, icosahedron , which yield regular meshes by straightforward projection, have been known for a long time (see for example [2, 3]) In the same way, sphere triangulations by congruent triangles have long been studied [5, 6, 8] Some of edge to edge triangulations involving isosceles triangles can be used to yield partitions by congruent (hence equal area) quadrilaterals. We cannot use these partitions because, either the ....

M. Berger. Geometry. Springer Verlag, Berlin, 1987.

Stratified Sampling of 2-Manifolds - James Arvo State (2001) Self-citation (Volume) (Correct)

....either for spherical triangles or projected spherical polygons, which will be described in the following section. Equation (1.36) is known as Girard s formula, equation (1.37) is the spherical law of sines, and equations (1.38) 1.39) and (1. 40) are spherical cosine laws for angles [4]. Our task will be to construct f : 0, 1] IR such that f(A s A) s, where the parameter s [0, 1] selects the sub triangle T s and consequently determines the area s . Specifically, the sub triangle T s is formed by choosing a new vertex C s on the great arc between A and C, at an arc ....

Marcel Berger. Geometry, volume II. Springer-Verlag, New York, 1987. Translated by M. Cole and S. Levy.

Unknown - (Correct)

No context found.

M. Berger, Geometry, Springer Verlag, Berlin (1987).

PhotoMeter: Easy-to-Use MonoGraphoMetrics - Visual Metrology from .. - Müller (2004) (Correct)

No context found.

M. BERGER. Geometry II. Springer-Verlag. 1987.

Learning an Intersection of a Constant Number of.. - Avrim Blum Ravindran (1997) (3 citations) (Correct)

No context found.

M. Berger. Geometry. Springer-Verlag, 1987.

Improved Approximation Algorithms for Maximum Cut and.. - Goemans, Williamson (1995) (389 citations) (Correct)

No context found.

M. Berger. Geometry II. Springer-Verlag, Berlin, 1987.

The Local Projective Shape of Smooth Surfaces and their Outlines - Lazebnik, Ponce (2003) (Correct)

No context found.

M. Berger. Geometry. Springer-Verlag, 1987.

Approximating MIN 2-SAT and MIN 3-SAT - Avidor, Zwick (Correct)

No context found.

M. Berger. Geometry II. Springer-Verlag, 1987.